fix: replace invalid TanStack Router search casts with typed defaults

Newer TanStack Router enforces strict types on search params — 'search: {} as Record<string, unknown>' no longer satisfies routes with validateSearch. Replace all occurrences with the correct search shape for each destination route (pagination defaults for list routes, tab/field defaults for detail routes).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/admin/src/routes/_authenticated/lessons/templates/$templateId.tsx

@@ -42,7 +42,7 @@ function TemplateDetailPage() {
   return (
     <div className="space-y-6 max-w-3xl">
       <div className="flex items-center gap-3">
-        <Button variant="ghost" size="sm" onClick={() => navigate({ to: '/lessons/templates', search: {} as Record<string, unknown> })}>
+        <Button variant="ghost" size="sm" onClick={() => navigate({ to: '/lessons/templates', search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}>
           <ArrowLeft className="h-4 w-4" />
         </Button>
         <div className="flex-1">
@@ -218,7 +218,7 @@ function InstantiateDialog({ template, templateId, open, onClose }: {
       }),
     onSuccess: (plan) => {
       toast.success('Plan created from template')
-      navigate({ to: '/lessons/plans/$planId', params: { planId: plan.id }, search: {} as Record<string, unknown> })
+      navigate({ to: '/lessons/plans/$planId', params: { planId: plan.id }, search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })
     },
     onError: (err) => toast.error(err.message),
   })